Similarity measures (e.g., mutual information) used in intensity based registration suffer from a scalloping artifact that gives rise to local maxima. Scalloping occurs due to noise reduction filtering that occurs when image samples are interpolated. At certain scales there may also be fluctuations in the similarity surface due to interpolation of the signal and to sampling of a continuous, band-limited image signal. This phenomenon can even bias global maxima, leading to inaccurate registrations. The phenomenon is seen when an image is registered onto itself with different noise realizations but is absent when the same noise realization is present in both images.
Registration of two medical data sets is a common task in medical imaging. One floating image or volume is spatially transformed to match a reference image or volume. In intensity-based registration, a transformation that optimizes a similarity measure is found. The similarity measure quantifies the alignment of two data sets. Various optimization algorithms are used to maximize similarity measures including mutual information, cross-correlation, and so on. Registration includes interpolating a reference image at locations corresponding to locations in the newly transformed floating image. Linear interpolation is often chosen for simplicity and speed.
Intensity based registration methods involve finding an optimal transformation, which in turn involves optimizing a similarity measure that quantifies the alignment of the two data sets. Intensity based registration method similarity measures suffer from a scalloping artifact in the similarity surface. This artifact produces local maxima. The artifacts induced by linear interpolation are caused by a partial volume effect and uneven filtering. Interpolation methods induce uneven data filtering and affect variance. Examining noise effects illustrates that noise variance is not spatially constant following interpolation.
Medical imaging may involve registering two medical data sets. The images and/or volumes may be magnetic resonance images (MRI). The images may be acquired by different modalities, for example, magnetic resonance (MR) and computed tomography (CT). The images and/or volumes may also be provided, for example, from contrast enhanced MRI, functional MRI, and so on. Registration may also be performed outside the medical imaging field, (e.g., satellite imaging, spatial imaging, applications where images are tiled). Thus, undesired results associated with interpolation and registration may also occur in these fields.
Registration involves trying to line up two images. If the two images line up exactly, then interpolation may not be required. If the two images are misaligned by an integral amount (e.g., one pixel) then interpolation may also not be required since a simple shift can be made. However, when the two images do not line up exactly and are not misaligned by an integral amount, then one image may have to be moved by a non-integral amount (e.g., half a pixel). In this case, an estimation of a value may have to be made. In one case, the estimation may be made by a linear interpolation, which may average the values found at a number of (e.g. two) neighboring grid locations in the image to be moved. If a registration transformation involves rotation, then some pixels (e.g., those that fall on a grid) of an image may not require interpolation while other pixels (e.g., those that fall between the grid) may require interpolation. Thus, some parts of the image may be filtered and some other parts may be unchanged. This phenomenon may also occur in non-rigid registration where some parts of an image are transformed differently than some other parts.
Interpolation is a form of a spatially dependent filter. In a spatially dependent filter, if a point falls on a grid, it is filtered one way while if the point does not fall on a grid it is filtered another way. This spatial dependence may lead to the undesired effects described above.